(a) Introduction.
(1) The desire to achieve educational excellence is
the driving force behind the Texas essential knowledge and skills
for mathematics, guided by the college and career readiness standards.
By embedding statistics, probability, and finance, while focusing
on computational thinking, mathematical fluency, and solid understanding,
Texas will lead the way in mathematics education and prepare all Texas
students for the challenges they will face in the 21st century.
(2) The process standards describe ways in which students
are expected to engage in the content. The placement of the process
standards at the beginning of the knowledge and skills listed for
each grade and course is intentional. The process standards weave
the other knowledge and skills together so that students may be successful
problem solvers and use mathematics efficiently and effectively in
daily life. The process standards are integrated at every grade level
and course. When possible, students will apply mathematics to problems
arising in everyday life, society, and the workplace. Students will
use a problemsolving model that incorporates analyzing given information,
formulating a plan or strategy, determining a solution, justifying
the solution, and evaluating the problemsolving process and the reasonableness
of the solution. Students will select appropriate tools such as real
objects, manipulatives, algorithms, paper and pencil, and technology
and techniques such as mental math, estimation, number sense, and
generalization and abstraction to solve problems. Students will effectively
communicate mathematical ideas, reasoning, and their implications
using multiple representations such as symbols, diagrams, graphs,
computer programs, and language. Students will use mathematical relationships
to generate solutions and make connections and predictions. Students
will analyze mathematical relationships to connect and communicate
mathematical ideas. Students will display, explain, or justify mathematical
ideas and arguments using precise mathematical language in written
or oral communication.
(3) The primary focal areas in Grade 8 are proportionality;
expressions, equations, relationships, and foundations of functions;
and measurement and data. Students use concepts, algorithms, and properties
of real numbers to explore mathematical relationships and to describe
increasingly complex situations. Students use concepts of proportionality
to explore, develop, and communicate mathematical relationships. Students
use algebraic thinking to describe how a change in one quantity in
a relationship results in a change in the other. Students connect
verbal, numeric, graphic, and symbolic representations of relationships,
including equations and inequalities. Students begin to develop an
understanding of functional relationships. Students use geometric
properties and relationships, as well as spatial reasoning, to model
and analyze situations and solve problems. Students communicate information
about geometric figures or situations by quantifying attributes, generalize
procedures from measurement experiences, and use the procedures to
solve problems. Students use appropriate statistics, representations
of data, and reasoning to draw conclusions, evaluate arguments, and
make recommendations. While the use of all types of technology is
important, the emphasis on algebra readiness skills necessitates the
implementation of graphing technology.
(4) Statements that contain the word "including" reference
content that must be mastered, while those containing the phrase "such
as" are intended as possible illustrative examples.
(b) Knowledge and skills.
(1) Mathematical process standards. The student uses
mathematical processes to acquire and demonstrate mathematical understanding.
The student is expected to:
(A) apply mathematics to problems arising in everyday
life, society, and the workplace;
(B) use a problemsolving model that incorporates analyzing
given information, formulating a plan or strategy, determining a solution,
justifying the solution, and evaluating the problemsolving process
and the reasonableness of the solution;
(C) select tools, including real objects, manipulatives,
paper and pencil, and technology as appropriate, and techniques, including
mental math, estimation, and number sense as appropriate, to solve
problems;
(D) communicate mathematical ideas, reasoning, and
their implications using multiple representations, including symbols,
diagrams, graphs, and language as appropriate;
(E) create and use representations to organize, record,
and communicate mathematical ideas;
(F) analyze mathematical relationships to connect and
communicate mathematical ideas; and
(G) display, explain, and justify mathematical ideas
and arguments using precise mathematical language in written or oral
communication.
(2) Number and operations. The student applies mathematical
process standards to represent and use real numbers in a variety of
forms. The student is expected to:
(A) extend previous knowledge of sets and subsets using
a visual representation to describe relationships between sets of
real numbers;
(B) approximate the value of an irrational number,
including π and square roots of numbers less than 225, and locate
that rational number approximation on a number line;
(C) convert between standard decimal notation and scientific
notation; and
(D) order a set of real numbers arising from mathematical
and realworld contexts.
(3) Proportionality. The student applies mathematical
process standards to use proportional relationships to describe dilations.
The student is expected to:
(A) generalize that the ratio of corresponding sides
of similar shapes are proportional, including a shape and its dilation;
(B) compare and contrast the attributes of a shape
and its dilation(s) on a coordinate plane; and
(C) use an algebraic representation to explain the
effect of a given positive rational scale factor applied to twodimensional
figures on a coordinate plane with the origin as the center of dilation.
(4) Proportionality. The student applies mathematical
process standards to explain proportional and nonproportional relationships
involving slope. The student is expected to:
(A) use similar right triangles to develop an understanding
that slope, m, given as the rate comparing
the change in y values to the change
in x values, (y_{2}  y_{1 }) / (x_{2}  x_{1 }), is the same for any two points (x_{1 }, y_{1 }) and (x_{2}, y_{2}) on the
same line;
(B) graph proportional relationships, interpreting
the unit rate as the slope of the line that models the relationship;
and
(C) use data from a table or graph to determine the
rate of change or slope and y intercept
in mathematical and realworld problems.
(5) Proportionality. The student applies mathematical
process standards to use proportional and nonproportional relationships
to develop foundational concepts of functions. The student is expected
to:
(A) represent linear proportional situations with tables,
graphs, and equations in the form of y =
kx;
(B) represent linear nonproportional situations with
tables, graphs, and equations in the form of y
= mx + b, where b ≠ 0;
(C) contrast bivariate sets of data that suggest a
linear relationship with bivariate sets of data that do not suggest
a linear relationship from a graphical representation;
(D) use a trend line that approximates the linear relationship
between bivariate sets of data to make predictions;
(E) solve problems involving direct variation;
(F) distinguish between proportional and nonproportional
situations using tables, graphs, and equations in the form y = kx or y = mx
+ b, where b ≠ 0;
(G) identify functions using sets of ordered pairs,
tables, mappings, and graphs;
(H) identify examples of proportional and nonproportional
functions that arise from mathematical and realworld problems; and
(I) write an equation in the form y = mx + b to model a linear relationship
between two quantities using verbal, numerical, tabular, and graphical
representations.
(6) Expressions, equations, and relationships. The
student applies mathematical process standards to develop mathematical
relationships and make connections to geometric formulas. The student
is expected to:
(A) describe the volume formula V
= Bh of a cylinder in terms of its base area and its height;
(B) model the relationship between the volume of a
cylinder and a cone having both congruent bases and heights and connect
that relationship to the formulas; and
(C) use models and diagrams to explain the Pythagorean
theorem.
(7) Expressions, equations, and relationships. The
student applies mathematical process standards to use geometry to
solve problems. The student is expected to:
(A) solve problems involving the volume of cylinders,
cones, and spheres;
(B) use previous knowledge of surface area to make
connections to the formulas for lateral and total surface area and
determine solutions for problems involving rectangular prisms, triangular
prisms, and cylinders;
(C) use the Pythagorean Theorem and its converse to
solve problems; and
(D) determine the distance between two points on a
coordinate plane using the Pythagorean Theorem.
(8) Expressions, equations, and relationships. The
student applies mathematical process standards to use onevariable
equations or inequalities in problem situations. The student is expected
to:
(A) write onevariable equations or inequalities with
variables on both sides that represent problems using rational number
coefficients and constants;
(B) write a corresponding realworld problem when given
a onevariable equation or inequality with variables on both sides
of the equal sign using rational number coefficients and constants;
(C) model and solve onevariable equations with variables
on both sides of the equal sign that represent mathematical and realworld
problems using rational number coefficients and constants; and
(D) use informal arguments to establish facts about
the angle sum and exterior angle of triangles, the angles created
when parallel lines are cut by a transversal, and the angleangle
criterion for similarity of triangles.
(9) Expressions, equations, and relationships. The
student applies mathematical process standards to use multiple representations
to develop foundational concepts of simultaneous linear equations.
The student is expected to identify and verify the values of x and y that
simultaneously satisfy two linear equations in the form y = mx + b from the intersections of the
graphed equations.
(10) Twodimensional shapes. The student applies mathematical
process standards to develop transformational geometry concepts. The
student is expected to:
(A) generalize the properties of orientation and congruence
of rotations, reflections, translations, and dilations of twodimensional
shapes on a coordinate plane;
(B) differentiate between transformations that preserve
congruence and those that do not;
(C) explain the effect of translations, reflections
over the x or y
axis, and rotations limited to 90°, 180°, 270°,
and 360° as applied to twodimensional shapes on a coordinate
plane using an algebraic representation; and
(D) model the effect on linear and area measurements
of dilated twodimensional shapes.
(11) Measurement and data. The student applies mathematical
process standards to use statistical procedures to describe data.
The student is expected to:
(A) construct a scatterplot and describe the observed
data to address questions of association such as linear, nonlinear,
and no association between bivariate data;
(B) determine the mean absolute deviation and use this
quantity as a measure of the average distance data are from the mean
using a data set of no more than 10 data points; and
(C) simulate generating random samples of the same
size from a population with known characteristics to develop the notion
of a random sample being representative of the population from which
it was selected.
(12) Personal financial literacy. The student applies
mathematical process standards to develop an economic way of thinking
and problem solving useful in one's life as a knowledgeable consumer
and investor. The student is expected to:
(A) solve realworld problems comparing how interest
rate and loan length affect the cost of credit;
(B) calculate the total cost of repaying a loan, including
credit cards and easy access loans, under various rates of interest
and over different periods using an online calculator;
(C) explain how small amounts of money invested regularly,
including money saved for college and retirement, grow over time;
(D) calculate and compare simple interest and compound
interest earnings;
(E) identify and explain the advantages and disadvantages
of different payment methods;
(F) analyze situations to determine if they represent
financially responsible decisions and identify the benefits of financial
responsibility and the costs of financial irresponsibility; and
(G) estimate the cost of a twoyear and fouryear college
education, including family contribution, and devise a periodic savings
plan for accumulating the money needed to contribute to the total
cost of attendance for at least the first year of college.
